Distributionally Robust Optimization for STAP With Finite Samples

Drawing on the minimization of worst-case maximum likelihood (ML) estimation, this paper develops a robust inverse clutter-plus-noise covariance matrix (CNCM) estimator for space-time adaptive processing against Gaussian clutter background at low sample support without any prior knowledge. Leveraging the nonconvex uncertainty set for CNCMs, we formulate a distributionally robust optimization-based ML estimation problem with the Wasserstein metric. We validate that the resulting nonconvex problem is algorithmically tractable. To achieve this, we reformulate the problem as a finite-dimensional semidefinite program. To pursue lower computational complexity, we establish a closed-form solution framework by imposing the rotation-equivariant property. We theoretically prove the existence and uniqueness of the solution and address the challenge of adaptively choosing the uncertainty set size. Importantly, the solution composes a nonlinear shrinkage estimator that inherently preserves the order of sample eigenvalues without additional operations. Experiments with both simulated and measured clutter data confirm the superiority of the proposed estimator in terms of estimation accuracy and robustness.